Details

sample300.0ms

Algorithm

intervals

Results

134.0ms	104×	body	1280	valid
73.0ms	54×	body	640	valid
51.0ms	19×	body	2560	valid
14.0ms	26×	body	320	valid
7.0ms	44×	body	80	valid
4.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize10.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (tan (+ x eps)) (tan x))
3.4b	(tan (+ x eps))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

56.0ms	(- (tan (+ x eps)) (tan x))
8.0ms	(tan (+ x eps))

series200.0ms

Counts

2 → 6

Calls

2 calls:

135.0ms	(- (tan (+ x eps)) (tan x))
65.0ms	(tan (+ x eps))

simplify2.4s

Counts

47 → 47

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	94	720
1	194	597
2	457	510
3	1461	450
done	5000	438

prune191.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

9.0ms	(+ (tan x) (tan eps))
32.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
16.0ms	(* (tan x) (tan eps))
189.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

157.0ms	(+ (tan x) (tan eps))
333.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
120.0ms	(* (tan x) (tan eps))
503.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.7s

Counts

181 → 181

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	240	4762
1	560	3970
2	1556	3555
done	5000	3149

prune558.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(fma (tan x) (- (tan eps)) 1)
0.1b	(/ (+ (tan x) (tan eps)) (fma (tan x) (- (tan eps)) 1))
2.6b	(- (* 1 (/ (+ (tan x) (tan eps)) (fma (tan x) (- (tan eps)) 1))) (tan x))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`tan-quot` `distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `prod-diff` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `associate-*r/` `div-exp` `clear-num` `sum-log` `frac-sub` `flip--` `fma-udef` `div-inv` `distribute-lft-out--`

Counts

4 → 84

Calls

4 calls:

20.0ms	(+ (tan x) (tan eps))
1.0ms	(fma (tan x) (- (tan eps)) 1)
61.0ms	(/ (+ (tan x) (tan eps)) (fma (tan x) (- (tan eps)) 1))
30.0ms	(- (* 1 (/ (+ (tan x) (tan eps)) (fma (tan x) (- (tan eps)) 1))) (tan x))

series1.3s

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (tan x) (tan eps))
192.0ms	(fma (tan x) (- (tan eps)) 1)
374.0ms	(/ (+ (tan x) (tan eps)) (fma (tan x) (- (tan eps)) 1))
601.0ms	(- (* 1 (/ (+ (tan x) (tan eps)) (fma (tan x) (- (tan eps)) 1))) (tan x))

simplify3.0s

Counts

96 → 96

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	163	1788
1	371	1649
2	1051	1549
3	3660	1523
done	5000	1522

prune435.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.6b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

16.0ms	(* (tan x) (tan eps))
17.0ms	(* (tan x) (tan eps))
94.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (tan x) (tan eps))
136.0ms	(* (tan x) (tan eps))
155.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
746.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify1.3s

Counts

119 → 119

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	158	1871
1	428	1759
2	1476	1476
done	5000	1399

prune519.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.1b

regimes191.0ms

Accuracy

86% (1.0b remaining)

Error of 15.5b against oracle of 14.4b and baseline of 21.8b

bsearch196.0ms

Steps

Iters	Range		Point
9	2.3625426050387105e-45	2.1992743221462194e-37	6.859816283499517e-40
3	-3.2222620239793486e-82	-2.300285317603571e-82	-3.143684469318109e-82

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	30	65
1	40	63
done	40	63

end0.0ms

sample9.8s

Algorithm

intervals

Results

5.6s	3378×	body	1280	valid
1.9s	611×	body	2560	valid
1.4s	1844×	body	640	valid
315.0ms	713×	body	320	valid
145.0ms	1105×	body	80	valid
140.0ms	349×	body	160	valid