Details

sample308.0ms

Algorithm

intervals

Results

141.0ms	113×	body	1280	valid
54.0ms	20×	body	2560	valid
44.0ms	25×	body	320	valid
41.0ms	55×	body	640	valid
6.0ms	15×	body	160	valid
4.0ms	28×	body	80	valid

simplify6.0ms

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: 37.0b

localize10.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (tan (+ x eps)) (tan x))
4.1b	(tan (+ x eps))

rewrite74.0ms

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:

32.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series596.0ms

Counts

2 → 6

Calls

2 calls:

502.0ms	(- (tan (+ x eps)) (tan x))
94.0ms	(tan (+ x eps))

simplify888.0ms

Counts

47 → 47

Iterations

Useful iterations: done (886.0ms)

Iter	Nodes	Cost
0	94	720
1	202	600
2	741	510
done	5001	450

prune173.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
3.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

87×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
59×	`add-cube-cbrt`
57×	`prod-diff`
49×	`times-frac`
21×	`fma-neg`
13×	`distribute-lft-out`
10×	`add-log-exp`
8×	`associate-/r/`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-def` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 151

Calls

4 calls:

8.0ms	(- 1 (* (tan x) (tan eps)))
9.0ms	(+ (tan x) (tan eps))
25.0ms	(* (tan x) (tan eps))
127.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

168.0ms	(- 1 (* (tan x) (tan eps)))
131.0ms	(+ (tan x) (tan eps))
168.0ms	(* (tan x) (tan eps))
545.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.2s

Counts

163 → 163

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	240	4204
1	582	3452
2	2637	3017
done	5000	3015

prune552.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 16.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.5b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite136.0ms

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:

19.0ms	(* (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
96.0ms	(* (* (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)))

series1.4s

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (tan x) (tan eps))
136.0ms	(* (tan x) (tan eps))
190.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
914.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify1.4s

Counts

119 → 119

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	158	1871
1	463	1759
2	2642	1498
done	5002	1472

prune613.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 16.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.5b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (log (exp (* (tan x) (tan eps))))) (- (tan x)))
3.9b	(log (exp (* (tan x) (tan eps))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
36×	`tan-quot`
18×	`add-exp-log` `frac-times` `pow-prod-down` `add-cbrt-cube`
12×	`associate-r/` `associate-l/`
9×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r` `associate-l` `pow-sqr` `pow-prod-up` `log1p-expm1-u`
3×	`log-prod` `log-pow`
2×	`pow-plus` `*-commutative`
1×	`pow2` `exp-prod` `exp-to-pow` `swap-sqr` `rem-log-exp` `fma-udef` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

20.0ms	(* (tan x) (tan eps))
88.0ms	(* (* (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 (log (exp (* (tan x) (tan eps))))) (- (tan x)))
8.0ms	(log (exp (* (tan x) (tan eps))))

series1.4s

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (tan x) (tan eps))
163.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
947.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (log (exp (* (tan x) (tan eps))))) (- (tan x)))
139.0ms	(log (exp (* (tan x) (tan eps))))

simplify1.9s

Counts

112 → 112

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	177	1885
1	515	1717
2	3025	1458
done	5000	1434

prune522.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 16.6b

regimes309.0ms

Accuracy

87.4% (0.9b remaining)

Error of 15.1b against oracle of 14.1b and baseline of 21.6b

bsearch280.0ms

Steps

Iters	Range		Point
6	5.657564454157724e-27	3.4928798111313496e-26	7.609705691109876e-27
8	-6.739795712749816e-68	-3.8540338292272195e-72	-1.0634119210767955e-69

simplify7.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	36	104
1	44	102
done	44	102

end0.0ms

sample11.8s

Algorithm

intervals

Results

5.3s	3304×	body	1280	valid
2.9s	609×	body	2560	valid
2.4s	1885×	body	640	valid
550.0ms	763×	body	320	valid
175.0ms	1085×	body	80	valid
117.0ms	354×	body	160	valid