Details

sample755.0ms

Algorithm

intervals

Results

352.0ms	53×	body	2560	valid
155.0ms	95×	body	1280	valid
42.0ms	51×	body	640	valid
17.0ms	34×	body	320	valid
5.0ms	13×	body	160	valid
5.0ms	10×	body	80	valid

simplify5.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (tan x))
1.6b	(- x (sin x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

51.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (tan x))
11.0ms	(- x (sin x))

series233.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(/ (- x (sin x)) (- x (tan x)))
70.0ms	(- x (tan x))
50.0ms	(- x (sin x))

simplify94.0ms

Counts: 89 → 89

prune303.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
16.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

25.0ms	(* 27/2800 (pow x 4))
14.0ms	(* 9/40 (pow x 2))
19.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series167.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* 27/2800 (pow x 4))
36.0ms	(* 9/40 (pow x 2))
62.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify145.0ms

Counts: 75 → 75

prune248.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

16.6b	(- (* 9/40 (pow x 2)) (+ (* (* (cbrt (* 27/2800 (pow x 4))) (cbrt (* 27/2800 (pow x 4)))) (cbrt (* 27/2800 (pow x 4)))) 1/2))
30.9b	(cbrt (* 27/2800 (pow x 4)))
30.9b	(cbrt (* 27/2800 (pow x 4)))
30.9b	(cbrt (* 27/2800 (pow x 4)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
2×	`diff-log`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

4 → 41

Calls

4 calls:

83.0ms	(- (* 9/40 (pow x 2)) (+ (* (* (cbrt (* 27/2800 (pow x 4))) (cbrt (* 27/2800 (pow x 4)))) (cbrt (* 27/2800 (pow x 4)))) 1/2))
9.0ms	(cbrt (* 27/2800 (pow x 4)))
10.0ms	(cbrt (* 27/2800 (pow x 4)))
10.0ms	(cbrt (* 27/2800 (pow x 4)))

series1.2s

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (* 9/40 (pow x 2)) (+ (* (* (cbrt (* 27/2800 (pow x 4))) (cbrt (* 27/2800 (pow x 4)))) (cbrt (* 27/2800 (pow x 4)))) 1/2))
383.0ms	(cbrt (* 27/2800 (pow x 4)))
319.0ms	(cbrt (* 27/2800 (pow x 4)))
348.0ms	(cbrt (* 27/2800 (pow x 4)))

simplify49.0ms

Counts: 53 → 53

prune224.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
2.1b	(log (exp (* 9/40 (pow x 2))))
18.4b	(- (log (exp (* 9/40 (pow x 2)))) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
15×	`-un-lft-identity` `associate-r*`
14×	`add-exp-log`
12×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
7×	`unswap-sqr`
6×	`pow1` `log-prod` `associate-l` `prod-exp`
4×	`log-pow` `sqr-pow`
3×	`associate--l+`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unpow2`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `rem-log-exp` `sum-log` `flip--` `associate--r+` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

24.0ms	(* 27/2800 (pow x 4))
17.0ms	(* 9/40 (pow x 2))
3.0ms	(log (exp (* 9/40 (pow x 2))))
51.0ms	(- (log (exp (* 9/40 (pow x 2)))) (+ (* 27/2800 (pow x 4)) 1/2))

series269.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* 27/2800 (pow x 4))
49.0ms	(* 9/40 (pow x 2))
52.0ms	(log (exp (* 9/40 (pow x 2))))
91.0ms	(- (log (exp (* 9/40 (pow x 2)))) (+ (* 27/2800 (pow x 4)) 1/2))

simplify120.0ms

Counts: 98 → 98

prune405.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes83.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.2b

bsearch143.0ms

Steps

Iters	Range		Point
10	1.5265582717444966e-05	421651.551737869	0.0323479305637792
9	-3616.0534617336225	-0.01082959410075795	-0.026506917744682296

simplify76.0ms

end0.0ms

sample13.5s

Algorithm

intervals

Results

5.7s	1619×	body	2560	valid
4.4s	2692×	body	1280	valid
1.5s	1888×	body	640	valid
881.0ms	901×	body	320	valid
565.0ms	407×	body	80	valid
149.0ms	493×	body	160	valid