Details

sample314.0ms

Algorithm

intervals

Results

191.0ms	105×	body	1280	valid
45.0ms	17×	body	2560	valid
41.0ms	59×	body	640	valid
11.0ms	24×	body	320	valid
6.0ms	42×	body	80	valid
3.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

25.0ms	(- (tan (+ x eps)) (tan x))
9.0ms	(tan (+ x eps))

series241.0ms

Counts

2 → 6

Calls

2 calls:

147.0ms	(- (tan (+ x eps)) (tan x))
94.0ms	(tan (+ x eps))

simplify1.8s

Counts

31 → 31

Iterations

Iter	Nodes
done	5001
4	1748
3	709
2	298
1	137
0	68

prune250.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `flip3--` `frac-add` `associate-/r/` `flip-+` `flip--` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

41.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
12.0ms	(+ (tan x) (tan eps))
22.0ms	(* (tan x) (tan eps))
100.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

299.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
145.0ms	(+ (tan x) (tan eps))
138.0ms	(* (tan x) (tan eps))
544.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.8s

Counts

98 → 98

Iterations

Iter	Nodes
done	5045
3	4214
2	1148
1	401
0	170

prune572.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.9b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
0.2b	(* (sin x) (/ (sin eps) (cos eps)))
0.2b	(* (sin x) (/ (sin eps) (cos eps)))
4.0b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
36×	`times-frac`
33×	`*-un-lft-identity`
26×	`associate-r`
23×	`add-cbrt-cube` `add-exp-log`
22×	`add-cube-cbrt`
8×	`pow1`
6×	`cbrt-undiv` `div-exp` `associate-l` `prod-exp` `cbrt-unprod` `add-log-exp` `difference-of-squares`
4×	`distribute-lft-out--` `unswap-sqr`
3×	`associate-/r` `associate-r/` `div-inv`
2×	`pow-prod-down` `*-commutative`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `frac-sub` `flip--` `associate-/l*` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

12.0ms	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
21.0ms	(* (sin x) (/ (sin eps) (cos eps)))
23.0ms	(* (sin x) (/ (sin eps) (cos eps)))
214.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
95.0ms	(* (sin x) (/ (sin eps) (cos eps)))
103.0ms	(* (sin x) (/ (sin eps) (cos eps)))
303.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify1.6s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	1612
1	484
0	186

prune947.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (/ (sin eps) (cos eps)))
0.2b	(* (sin x) (/ (sin eps) (cos eps)))
4.0b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (log (exp (* (sin x) (/ (sin eps) (cos eps))))) (cos x)))) (/ (sin x) (cos x)))
4.2b	(log (exp (* (sin x) (/ (sin eps) (cos eps)))))

rewrite470.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
33×	`times-frac`
32×	`*-un-lft-identity`
26×	`associate-r`
21×	`add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
7×	`add-log-exp`
6×	`associate-l` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
3×	`log-prod` `log-pow`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `rem-log-exp` `frac-sub` `flip--`

Counts

4 → 100

Calls

4 calls:

30.0ms	(* (sin x) (/ (sin eps) (cos eps)))
31.0ms	(* (sin x) (/ (sin eps) (cos eps)))
395.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (log (exp (* (sin x) (/ (sin eps) (cos eps))))) (cos x)))) (/ (sin x) (cos x)))
6.0ms	(log (exp (* (sin x) (/ (sin eps) (cos eps)))))

series758.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (sin x) (/ (sin eps) (cos eps)))
119.0ms	(* (sin x) (/ (sin eps) (cos eps)))
380.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (log (exp (* (sin x) (/ (sin eps) (cos eps))))) (cos x)))) (/ (sin x) (cos x)))
152.0ms	(log (exp (* (sin x) (/ (sin eps) (cos eps)))))

simplify2.0s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1193
1	403
0	168

prune975.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.9b

regimes220.0ms

Accuracy

0% (0.4b remaining)

Error of 13.0b against oracle of 12.6b and baseline of 13.0b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	24
1	24
0	20

end0.0ms

sample10.0s

Algorithm

intervals

Results

4.2s	3251×	body	1280	valid
2.3s	1865×	body	640	valid
2.1s	650×	body	2560	valid
758.0ms	772×	body	320	valid
154.0ms	1137×	body	80	valid
91.0ms	325×	body	160	valid